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# In a certain math class, one-tenth of the students cheated on a test

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Math Expert
Joined: 02 Sep 2009
Posts: 52390
In a certain math class, one-tenth of the students cheated on a test  [#permalink]

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01 Apr 2017, 06:13
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Difficulty:

95% (hard)

Question Stats:

41% (02:25) correct 59% (01:29) wrong based on 136 sessions

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In a certain math class, one-tenth of the students cheated on a test and were caught but one-fifth of the students who cheated did not get caught. What fraction of the class cheated on the test?

A. 21/100
B. 1/10
C. 1/8
D. 3/10
E. 4/5

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Re: In a certain math class, one-tenth of the students cheated on a test  [#permalink]

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01 Apr 2017, 06:28
1
10% cheated and got caught
20% Cheated did not get caught
so, total 30% cheated=3/10 is the answer
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Re: In a certain math class, one-tenth of the students cheated on a test  [#permalink]

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01 Apr 2017, 06:53
1
Bunuel wrote:
In a certain math class, one-tenth of the students cheated on a test and were caught but one-fifth of the students who cheated did not get caught. What fraction of the class cheated on the test?

A. 21/100
B. 1/10
C. 1/8
D. 3/10
E. 4/5

Say there are 100 students and 'x' of them cheated
So the que basically asks what is x/100?

one-tenth of the students cheated on a test and were caught
1/10 *(100)-cheated and caught-1
but one-fifth of the students who cheated did not get caught
so 4/5x of the students cheated and were caught-2

Equating 1 and 2
10=4/5x
x=50/4

x/100=1/8

Ans:C
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Re: In a certain math class, one-tenth of the students cheated on a test  [#permalink]

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01 Apr 2017, 07:01
Top Contributor
Bunuel wrote:
In a certain math class, one-tenth of the students cheated on a test and were caught but one-fifth of the students who cheated did not get caught. What fraction of the class cheated on the test?

A. 21/100
B. 1/10
C. 1/8
D. 3/10
E. 4/5

TOTAL number of cheaters = (# of people who cheated AND got caught) + (# of people who cheated AND DID NOT get caught)

To make things easier, let's say there are 100 people in the math class.
Let x = TOTAL number of cheaters

one-tenth of the students cheated on a test and were caught
1/10 of 100 = 10, so 10 people cheated AND got caught

one-fifth of the students who cheated did not get caught
In other words, 1/5 of x = number of students who cheated and DID NOT get caught
Rewrite as: 0.2x = number of students who cheated and DID NOT get caught

Plug all values into original equation: TOTAL number of cheaters = (# of people who cheated AND got caught) + (# of people who cheated AND DID NOT get caught)
We get; x = 10 + 0.2x
Subtract 0.2x from both sides: 0.8x = 10
Solve: x = 12.5

What fraction of the class cheated on the test?
If there are 100 people in the class, and 12.5 of them cheated, then the fraction of the class who cheated on the test = 12.5/100 = 1/8

Cheers,
Brent
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Joined: 21 Mar 2016
Posts: 523
Re: In a certain math class, one-tenth of the students cheated on a test  [#permalink]

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02 Apr 2017, 06:18
1
lets say total number of students = X.
1/10 of X were cheated and caught..

let say y cheated,,, 4/5 of y cheated and were caught..

(1/10) of X = 4/5 of Y

Y/X = 1/8

ans C
Intern
Joined: 23 Mar 2017
Posts: 6
Re: In a certain math class, one-tenth of the students cheated on a test  [#permalink]

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04 Apr 2017, 19:12
Using pick numbers, assume 120 students total.

120 * 10% cheated and got caught = 12 students
1/5 of students who cheated did not get caught so 4/5 of students who cheated got caught
12 students = 4/5 * total cheaters = 15 total cheaters
15/120 = 1/8 were cheaters

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Re: In a certain math class, one-tenth of the students cheated on a test  [#permalink]

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07 Jun 2018, 16:05
Bunuel wrote:
In a certain math class, one-tenth of the students cheated on a test and were caught but one-fifth of the students who cheated did not get caught. What fraction of the class cheated on the test?

A. 21/100
B. 1/10
C. 1/8
D. 3/10
E. 4/5

We can let the number of students in the class be 80, so 8 students cheated and were caught. However, since 1/5 of the students who cheated were not caught, the 8 students who were caught must represent 4/5 of students who cheated. Thus if we let n = number of students who cheated, we have: We can let n = the total number of students who cheated n/10 cheated and were caught, so 9n/10 were not caught.

(4/5)n = 8

n = 10

Therefore, 10 out of 80 students cheated, which is 10/80 = 1/8 of the class.

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Re: In a certain math class, one-tenth of the students cheated on a test &nbs [#permalink] 07 Jun 2018, 16:05
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